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FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

In the Vasicek model, a European call option on a zero-coupon bond is priced with a Black-type closed-form formula. Which input to that formula is determined by the model's interest rate volatility and mean reversion rather than being directly observed as a single market volatility?

The bond price volatility used in the Vasicek zero-coupon bond option formula is implied by σ, the mean reversion speed k, and the option and bond maturities. Strike, expiry and current bond prices are directly observable, whereas the effective volatility comes from the model's rate dynamics.

  1. AThe strike price of the option
  2. BThe bond price volatility, which depends on σ and the time structure of kCorrect
  3. CThe option's time to expiry only
  4. DThe current zero-coupon bond price

Explanation

The Vasicek bond option formula uses a bond price volatility derived from σ, k, option maturity T, and bond maturity s, via the factor (1−e^{−k(s−T)})/k times σ√((1−e^{−2kT})/(2k)). Strike, expiry, and the current bond prices are observable inputs, not derived from the rate dynamics.

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